Question 28412: how do you figure out the factors of a number and how do you know if it is prime or not?
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! Primes
Any number can be written as a set of prime numbers multiplied together. You need to know the first few primes... 2,3,5,7,11,13,... The majority of work in this area will give you numbers that factorise into these numbers. Higher primes are too much work for students in exam conditions.
FACTOR of 2:
Is it even? if so, 2 is a factor eg 236 --> 2*118
FACTOR of 3:
When you add up the digits, is that number divisible by 3? If so, the original number has 3 as a factor eg 351 --> 3+5+1=9 and 3 goes into 9, so 351 --> 3*117
FACTOR of 5:
Is the last digit a 5 or a 0? If so, 5 is a factor eg 235 --> 5*47.
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Example:
Write 27027 as a set of factors.
Method:
Start with 2, the look for 3 then 5 and keep keep working at the number with ever increasing primes:
The number is odd, so 2 is not a factor.
Add up the digits: 2+7+0+2+7=18 --> 18 divides by 3 so 3 is a factor --> 3*9009
Now look at 9009 --> 9+0+0+9 = 18 which again divides by 3, so we have 3*3*3003
Similar process... 3*3*3*1001
Now 1+0+0+1=2... and 2 does not divide by 3.
So lets move onto 5. last digit is not 5 or 0 so 5 is not a factor.
How about 7? Divide it and see. Yes --> 3*3*3*7*143
143/7? No,
So next is 11. Yes --> 3*3*3*7*11*13
Finally 13 is a prime so that is it. Final answer is 3*3*3*7*11*13.
jon.
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